Advanced PDE

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Advanced PDE


This course will propose to study non-linear parabolic problems by the way of variational type techniques. A first approach of the type changing problems will be considered. The case of first order hyperbolic problems will be presented.

Number of hours

  • Cours Magistral : 27h
  • Travaux Dirigés : 12h

Form of assessment

First session

Second session

Final assessment: 100%

Final assessment length: 3 hours

Remedial assessment: 100 %

Remedial assessment length: 3 hours


1) Vector valued distributions, spaces L^p(0,T,V) and W(0,T).

2) Non-degenerate parabolic problems: fixed-point theorems, time discretisation, and compactness.

3) Degenerate parabolic problems: artificial viscosity method.

4) First order hyperbolic problems in R, then in a bounded domain: characteristics method, notions of weak solution and entropy solutions.

5) First order hyperbolic problems in R^n: doubling variable method for uniqueness.

6) Existence via an artificial viscosity method.

Additional information


Dautray Lions : Analyse mathématique et calcul numérique.

Brézis : Functional analysis.

Evans : Partial Differential Equations.

In brief

ECTS credits 4.0

Number of hours 39.0

Level of study Master degree level


Organizational unit

Person in charge(s)

Vallet Guy

Email : guy.vallet @

LEVI Laurent

Email : laurent.levi @

Administrative contact(s)

Secrétariat de Mathématiques

Email : secretariat-mathematiques @


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